Here is a particular code. Can anyone please help me in taking the analytical (partial) derivative of the function ‘F’ along X (i.e., w.r.t. X) along Y (i.e., w.r.t. Y) and along the diagonal (i.e., w.r.t. X plus w.r.t. Y) using matlab command.

[X, Y]=meshgrid(-1:2/511:+1, -1:2/511:+1);
F=sqrt(3).*(2.*(X.^2+Y.^2)-1);

Thanking You!Here is a particular code. Can anyone please help me in taking the analytical (partial) derivative of the function ‘F’ along X (i.e., w.r.t. X) along Y (i.e., w.r.t. Y) and along the diagonal (i.e., w.r.t. X plus w.r.t. Y) using matlab command.

[X, Y]=meshgrid(-1:2/511:+1, -1:2/511:+1);
F=sqrt(3).*(2.*(X.^2+Y.^2)-1);

Thanking You! Here is a particular code. Can anyone please help me in taking the analytical (partial) derivative of the function ‘F’ along X (i.e., w.r.t. X) along Y (i.e., w.r.t. Y) and along the diagonal (i.e., w.r.t. X plus w.r.t. Y) using matlab command.

[X, Y]=meshgrid(-1:2/511:+1, -1:2/511:+1);
F=sqrt(3).*(2.*(X.^2+Y.^2)-1);

Thanking You! differential equations MATLAB Answers — New Questions

​

I wrote a simple code that calculates the covariance of images along different directions and lag spacings and returns a 2D map of covariance values varying by lags(h1,h2). The original program I wrote accepts only 2D inputs:
function [Correlogram] = ExhaustiveCovarianceFunction(X,lags)
[ny,nx,~]=size(X);
Covariance=NaN([2*lags+1 2*lags+1]);
Correlogram=NaN([2*lags+1 2*lags+1]);
for hy=-lags:lags
for hx=-lags:lags

sumprod=0;
sum1=0;
sum2=0;
countpairs=0;
for j=1:ny
for i=1:nx
if hy+j<=0 || hy+j>ny || hx+i<=0 || hx+i>nx
countpairs=countpairs;
continue

else
sumprod=X(j,i)*X(j+hy,i+hx) + sumprod;
sum1=X(j,i) + sum1;
sum2=X(j+hy,i+hx) + sum2;
countpairs=countpairs+1;
end
end
end

sumprod=sumprod/(countpairs);
sum1=sum1/(countpairs);
sum2=sum2/(countpairs);
Covariance(hy+lags+1,hx+lags+1)=sumprod – sum1*sum2;

%Standardize covariance values to correlogram
mean1=sum1;
mean2=sum2;
countpairs=0;
sumvar1=0;
sumvar2=0;
for j=1:ny
for i=1:nx
if hy+j<=0 || hy+j>ny || hx+i<=0 || hx+i>nx
continue

else
sumvar1=(X(j,i)-mean1)^2 + sumvar1;
sumvar2=(X(j+hy,i+hx)-mean2)^2 + sumvar2;
countpairs=countpairs+1;
end
end
end

sumvar1=sumvar1/countpairs;
sumvar2=sumvar2/countpairs;

Correlogram(hy+lags+1,hx+lags+1)=Covariance(hy+lags+1,hx+lags+1)/sqrt(sumvar1*sumvar2);

end
end
end

I wanted to extend this code to allow for up to 3D image inputs, but also allow 2D or 1D inputs. Some other changes for optimization were made (dynamically updating bounds, removing if/else statement):
function [Correlogram] = ExhaustiveCovarianceFunction3D(X,lags)
[ny,nx,nz]=size(X);
%lags is now a vector
Covariance=NaN([2*lags(1)+1, 2*lags(2)+1, 2*lags(3)+1]);
Correlogram=NaN([2*lags(1)+1, 2*lags(2)+1, 2*lags(3)+1]);

for hz=-lags(3):lags(3)
for hy=-lags(1):lags(1)
for hx=-lags(2):lags(2)

hvector = [hy hx hz];

if hvector(1)<0
ymin=abs(hvector(1))+1;
ymax=ny;
else
ymin=1;
ymax=ny-hvector(1);
end

if hvector(2)<0
xmin=abs(hvector(2))+1;
xmax=nx;
else
xmin=1;
xmax=nx-hvector(2);
end

if hvector(3)<0
zmin=abs(hvector(3))+1;
zmax=nz;
else
zmin=1;
zmax=nz-hvector(3);
end

sumprod=0;
sum1=0;
sum2=0;
for k=zmin:zmax
for j=ymin:ymax
for i=xmin:xmax
sumprod=X(j,i,k)*X(j+hy,i+hx,k+hz) + sumprod;
sum1=X(j,i,k) + sum1;
sum2=X(j+hy,i+hx,k+hz) + sum2;
end
end
end

countpairs = numel(ymin:ymax)*numel(xmin:xmax)*numel(zmin:zmax);
sumprod=sumprod/(countpairs);
sum1=sum1/(countpairs);
sum2=sum2/(countpairs);
Covariance(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)=sumprod – sum1*sum2;

%Standardize covariance values to correlogram
mean1=sum1;
mean2=sum2;
sumvar1=0;
sumvar2=0;
for k=zmin:zmax
for j=ymin:ymax
for i=xmin:xmax

sumvar1=(X(j,i,k)-mean1)^2 + sumvar1;
sumvar2=(X(j+hy,i+hx,k+hz)-mean2)^2 + sumvar2;

end
end
end

sumvar1=sumvar1/countpairs;
sumvar2=sumvar2/countpairs;

Correlogram(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)=Covariance(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)/sqrt(sumvar1*sumvar2);

end
end
end
end

I first compared these codes for a 2D input image (nz=1) and noticed that my new function runs much slower than the original function:
ExhaustiveCovarianceFunction(testslice,25): Elapsed time is 0.057659 seconds.
ExhaustiveCovarianceFunction3D(testslice,[25,25,0]): Elapsed time is 19.251866 seconds.
After some testing, this led me to realize that indexing a 3D array is much slower than a 2D array in MATLAB, and that this has something to do with how memory is accessed for higher-dimensional arrays. I found out that, if I added a third dimension to the original ExhaustiveCovarianceFunction with index 1 that never changed (eg, X(j,i,1), with no other changes, the code slowed down significantly:
2D array index X(j,i): Elapsed time is 0.059815 seconds.
3D array index X(j,i,1): Elapsed time is 18.849217 seconds.
The idea that we cannot work with higher-dimensional arrays in MATLAB if we want to have optimal performance led me to an approach where, in my new function, I convert the 2D and 3D arrays to a 1D array and map the nD array indices to 1D:
function index1D = convert3Dto1D_index(j, i, k, ny, nx)
index1D = j + (i – 1) * ny + (k – 1) * ny * nx;
end

function [Correlogram] = ExhaustiveCovarianceFunction3D(Xinput,lags)

X = flatten3D(Xinput);

[ny,nx,nz]=size(Xinput);

%lags is now a vector
Covariance=NaN([2*lags(1)+1, 2*lags(2)+1, 2*lags(3)+1]);
Correlogram=NaN([2*lags(1)+1, 2*lags(2)+1, 2*lags(3)+1]);

for hz=-lags(3):lags(3)
for hy=-lags(1):lags(1)
for hx=-lags(2):lags(2)

hvector = [hy hx hz];

if hvector(1)<0
ymin=abs(hvector(1))+1;
ymax=ny;
else
ymin=1;
ymax=ny-hvector(1);
end

if hvector(2)<0
xmin=abs(hvector(2))+1;
xmax=nx;
else
xmin=1;
xmax=nx-hvector(2);
end

if hvector(3)<0
zmin=abs(hvector(3))+1;
zmax=nz;
else
zmin=1;
zmax=nz-hvector(3);
end

sumprod=0;
sum1=0;
sum2=0;
countpairs=0;
for k=zmin:zmax
for j=ymin:ymax
for i=xmin:xmax
sumprod=X(convert3Dto1D_index(j, i, k, ny, nx))*X(convert3Dto1D_index(j+hy, i+hx, k+hz, ny, nx)) + sumprod;
sum1=X(convert3Dto1D_index(j, i, k, ny, nx)) + sum1;
sum2=X(convert3Dto1D_index(j+hy, i+hx, k+hz, ny, nx)) + sum2;
countpairs=countpairs+1;
end
end
end

countpairs = numel(ymin:ymax)*numel(xmin:xmax)*numel(zmin:zmax);
sumprod=sumprod/(countpairs);
sum1=sum1/(countpairs);
sum2=sum2/(countpairs);
Covariance(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)=sumprod – sum1*sum2;

%Standardize covariance values to correlogram
mean1=sum1;
mean2=sum2;
sumvar1=0;
sumvar2=0;
for k=zmin:zmax
for j=ymin:ymax
for i=xmin:xmax

sumvar1=(X(convert3Dto1D_index(j, i, k, ny, nx))-mean1)^2 + sumvar1;
sumvar2=(X(convert3Dto1D_index(j+hy, i+hx, k+hz, ny, nx))-mean2)^2 + sumvar2;

end
end
end

sumvar1=sumvar1/countpairs;
sumvar2=sumvar2/countpairs;

Correlogram(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)=Covariance(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)/sqrt(sumvar1*sumvar2);

end
end
end
end
This approach has better performance, but is still slower than the original 2D code:
2D: Elapsed time is 0.163243 seconds.
3D, 3D index: Elapsed time is 18.336108 seconds.
3D, 1D index: Elapsed time is 0.431890 seconds.
The optimized code with 1D array indexing is still about 3x slower. Perhaps calling convert3Dto1D_index(j, i, k, ny, nx) every time the image index is called is leading to this expense.These computational concerns are important for larger images (eg, 256x256x128) and for higher-order statistics that will be developed.
Is there a smarter approach to addressing this problem? I cannot figure out how to speed up this 3D code any more. Ideally, I seek to make the 3D/general code to have comparable speeds to the 2D "hard-coded" problem when a 2D image is input. If this is not possible, separate subroutines for 2D and 3D images is likely my best bet.I wrote a simple code that calculates the covariance of images along different directions and lag spacings and returns a 2D map of covariance values varying by lags(h1,h2). The original program I wrote accepts only 2D inputs:
function [Correlogram] = ExhaustiveCovarianceFunction(X,lags)
[ny,nx,~]=size(X);
Covariance=NaN([2*lags+1 2*lags+1]);
Correlogram=NaN([2*lags+1 2*lags+1]);
for hy=-lags:lags
for hx=-lags:lags

sumprod=0;
sum1=0;
sum2=0;
countpairs=0;
for j=1:ny
for i=1:nx
if hy+j<=0 || hy+j>ny || hx+i<=0 || hx+i>nx
countpairs=countpairs;
continue

else
sumprod=X(j,i)*X(j+hy,i+hx) + sumprod;
sum1=X(j,i) + sum1;
sum2=X(j+hy,i+hx) + sum2;
countpairs=countpairs+1;
end
end
end

sumprod=sumprod/(countpairs);
sum1=sum1/(countpairs);
sum2=sum2/(countpairs);
Covariance(hy+lags+1,hx+lags+1)=sumprod – sum1*sum2;

%Standardize covariance values to correlogram
mean1=sum1;
mean2=sum2;
countpairs=0;
sumvar1=0;
sumvar2=0;
for j=1:ny
for i=1:nx
if hy+j<=0 || hy+j>ny || hx+i<=0 || hx+i>nx
continue

else
sumvar1=(X(j,i)-mean1)^2 + sumvar1;
sumvar2=(X(j+hy,i+hx)-mean2)^2 + sumvar2;
countpairs=countpairs+1;
end
end
end

sumvar1=sumvar1/countpairs;
sumvar2=sumvar2/countpairs;

Correlogram(hy+lags+1,hx+lags+1)=Covariance(hy+lags+1,hx+lags+1)/sqrt(sumvar1*sumvar2);

end
end
end

I wanted to extend this code to allow for up to 3D image inputs, but also allow 2D or 1D inputs. Some other changes for optimization were made (dynamically updating bounds, removing if/else statement):
function [Correlogram] = ExhaustiveCovarianceFunction3D(X,lags)
[ny,nx,nz]=size(X);
%lags is now a vector
Covariance=NaN([2*lags(1)+1, 2*lags(2)+1, 2*lags(3)+1]);
Correlogram=NaN([2*lags(1)+1, 2*lags(2)+1, 2*lags(3)+1]);

for hz=-lags(3):lags(3)
for hy=-lags(1):lags(1)
for hx=-lags(2):lags(2)

hvector = [hy hx hz];

if hvector(1)<0
ymin=abs(hvector(1))+1;
ymax=ny;
else
ymin=1;
ymax=ny-hvector(1);
end

if hvector(2)<0
xmin=abs(hvector(2))+1;
xmax=nx;
else
xmin=1;
xmax=nx-hvector(2);
end

if hvector(3)<0
zmin=abs(hvector(3))+1;
zmax=nz;
else
zmin=1;
zmax=nz-hvector(3);
end

sumprod=0;
sum1=0;
sum2=0;
for k=zmin:zmax
for j=ymin:ymax
for i=xmin:xmax
sumprod=X(j,i,k)*X(j+hy,i+hx,k+hz) + sumprod;
sum1=X(j,i,k) + sum1;
sum2=X(j+hy,i+hx,k+hz) + sum2;
end
end
end

countpairs = numel(ymin:ymax)*numel(xmin:xmax)*numel(zmin:zmax);
sumprod=sumprod/(countpairs);
sum1=sum1/(countpairs);
sum2=sum2/(countpairs);
Covariance(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)=sumprod – sum1*sum2;

%Standardize covariance values to correlogram
mean1=sum1;
mean2=sum2;
sumvar1=0;
sumvar2=0;
for k=zmin:zmax
for j=ymin:ymax
for i=xmin:xmax

sumvar1=(X(j,i,k)-mean1)^2 + sumvar1;
sumvar2=(X(j+hy,i+hx,k+hz)-mean2)^2 + sumvar2;

end
end
end

sumvar1=sumvar1/countpairs;
sumvar2=sumvar2/countpairs;

Correlogram(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)=Covariance(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)/sqrt(sumvar1*sumvar2);

end
end
end
end

I first compared these codes for a 2D input image (nz=1) and noticed that my new function runs much slower than the original function:
ExhaustiveCovarianceFunction(testslice,25): Elapsed time is 0.057659 seconds.
ExhaustiveCovarianceFunction3D(testslice,[25,25,0]): Elapsed time is 19.251866 seconds.
After some testing, this led me to realize that indexing a 3D array is much slower than a 2D array in MATLAB, and that this has something to do with how memory is accessed for higher-dimensional arrays. I found out that, if I added a third dimension to the original ExhaustiveCovarianceFunction with index 1 that never changed (eg, X(j,i,1), with no other changes, the code slowed down significantly:
2D array index X(j,i): Elapsed time is 0.059815 seconds.
3D array index X(j,i,1): Elapsed time is 18.849217 seconds.
The idea that we cannot work with higher-dimensional arrays in MATLAB if we want to have optimal performance led me to an approach where, in my new function, I convert the 2D and 3D arrays to a 1D array and map the nD array indices to 1D:
function index1D = convert3Dto1D_index(j, i, k, ny, nx)
index1D = j + (i – 1) * ny + (k – 1) * ny * nx;
end

function [Correlogram] = ExhaustiveCovarianceFunction3D(Xinput,lags)

X = flatten3D(Xinput);

[ny,nx,nz]=size(Xinput);

%lags is now a vector
Covariance=NaN([2*lags(1)+1, 2*lags(2)+1, 2*lags(3)+1]);
Correlogram=NaN([2*lags(1)+1, 2*lags(2)+1, 2*lags(3)+1]);

for hz=-lags(3):lags(3)
for hy=-lags(1):lags(1)
for hx=-lags(2):lags(2)

hvector = [hy hx hz];

if hvector(1)<0
ymin=abs(hvector(1))+1;
ymax=ny;
else
ymin=1;
ymax=ny-hvector(1);
end

if hvector(2)<0
xmin=abs(hvector(2))+1;
xmax=nx;
else
xmin=1;
xmax=nx-hvector(2);
end

if hvector(3)<0
zmin=abs(hvector(3))+1;
zmax=nz;
else
zmin=1;
zmax=nz-hvector(3);
end

sumprod=0;
sum1=0;
sum2=0;
countpairs=0;
for k=zmin:zmax
for j=ymin:ymax
for i=xmin:xmax
sumprod=X(convert3Dto1D_index(j, i, k, ny, nx))*X(convert3Dto1D_index(j+hy, i+hx, k+hz, ny, nx)) + sumprod;
sum1=X(convert3Dto1D_index(j, i, k, ny, nx)) + sum1;
sum2=X(convert3Dto1D_index(j+hy, i+hx, k+hz, ny, nx)) + sum2;
countpairs=countpairs+1;
end
end
end

countpairs = numel(ymin:ymax)*numel(xmin:xmax)*numel(zmin:zmax);
sumprod=sumprod/(countpairs);
sum1=sum1/(countpairs);
sum2=sum2/(countpairs);
Covariance(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)=sumprod – sum1*sum2;

%Standardize covariance values to correlogram
mean1=sum1;
mean2=sum2;
sumvar1=0;
sumvar2=0;
for k=zmin:zmax
for j=ymin:ymax
for i=xmin:xmax

sumvar1=(X(convert3Dto1D_index(j, i, k, ny, nx))-mean1)^2 + sumvar1;
sumvar2=(X(convert3Dto1D_index(j+hy, i+hx, k+hz, ny, nx))-mean2)^2 + sumvar2;

end
end
end

sumvar1=sumvar1/countpairs;
sumvar2=sumvar2/countpairs;

Correlogram(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)=Covariance(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)/sqrt(sumvar1*sumvar2);

end
end
end
end
This approach has better performance, but is still slower than the original 2D code:
2D: Elapsed time is 0.163243 seconds.
3D, 3D index: Elapsed time is 18.336108 seconds.
3D, 1D index: Elapsed time is 0.431890 seconds.
The optimized code with 1D array indexing is still about 3x slower. Perhaps calling convert3Dto1D_index(j, i, k, ny, nx) every time the image index is called is leading to this expense.These computational concerns are important for larger images (eg, 256x256x128) and for higher-order statistics that will be developed.
Is there a smarter approach to addressing this problem? I cannot figure out how to speed up this 3D code any more. Ideally, I seek to make the 3D/general code to have comparable speeds to the 2D "hard-coded" problem when a 2D image is input. If this is not possible, separate subroutines for 2D and 3D images is likely my best bet. I wrote a simple code that calculates the covariance of images along different directions and lag spacings and returns a 2D map of covariance values varying by lags(h1,h2). The original program I wrote accepts only 2D inputs:
function [Correlogram] = ExhaustiveCovarianceFunction(X,lags)
[ny,nx,~]=size(X);
Covariance=NaN([2*lags+1 2*lags+1]);
Correlogram=NaN([2*lags+1 2*lags+1]);
for hy=-lags:lags
for hx=-lags:lags

sumprod=0;
sum1=0;
sum2=0;
countpairs=0;
for j=1:ny
for i=1:nx
if hy+j<=0 || hy+j>ny || hx+i<=0 || hx+i>nx
countpairs=countpairs;
continue

else
sumprod=X(j,i)*X(j+hy,i+hx) + sumprod;
sum1=X(j,i) + sum1;
sum2=X(j+hy,i+hx) + sum2;
countpairs=countpairs+1;
end
end
end

sumprod=sumprod/(countpairs);
sum1=sum1/(countpairs);
sum2=sum2/(countpairs);
Covariance(hy+lags+1,hx+lags+1)=sumprod – sum1*sum2;

%Standardize covariance values to correlogram
mean1=sum1;
mean2=sum2;
countpairs=0;
sumvar1=0;
sumvar2=0;
for j=1:ny
for i=1:nx
if hy+j<=0 || hy+j>ny || hx+i<=0 || hx+i>nx
continue

else
sumvar1=(X(j,i)-mean1)^2 + sumvar1;
sumvar2=(X(j+hy,i+hx)-mean2)^2 + sumvar2;
countpairs=countpairs+1;
end
end
end

sumvar1=sumvar1/countpairs;
sumvar2=sumvar2/countpairs;

Correlogram(hy+lags+1,hx+lags+1)=Covariance(hy+lags+1,hx+lags+1)/sqrt(sumvar1*sumvar2);

end
end
end

I wanted to extend this code to allow for up to 3D image inputs, but also allow 2D or 1D inputs. Some other changes for optimization were made (dynamically updating bounds, removing if/else statement):
function [Correlogram] = ExhaustiveCovarianceFunction3D(X,lags)
[ny,nx,nz]=size(X);
%lags is now a vector
Covariance=NaN([2*lags(1)+1, 2*lags(2)+1, 2*lags(3)+1]);
Correlogram=NaN([2*lags(1)+1, 2*lags(2)+1, 2*lags(3)+1]);

for hz=-lags(3):lags(3)
for hy=-lags(1):lags(1)
for hx=-lags(2):lags(2)

hvector = [hy hx hz];

if hvector(1)<0
ymin=abs(hvector(1))+1;
ymax=ny;
else
ymin=1;
ymax=ny-hvector(1);
end

if hvector(2)<0
xmin=abs(hvector(2))+1;
xmax=nx;
else
xmin=1;
xmax=nx-hvector(2);
end

if hvector(3)<0
zmin=abs(hvector(3))+1;
zmax=nz;
else
zmin=1;
zmax=nz-hvector(3);
end

sumprod=0;
sum1=0;
sum2=0;
for k=zmin:zmax
for j=ymin:ymax
for i=xmin:xmax
sumprod=X(j,i,k)*X(j+hy,i+hx,k+hz) + sumprod;
sum1=X(j,i,k) + sum1;
sum2=X(j+hy,i+hx,k+hz) + sum2;
end
end
end

countpairs = numel(ymin:ymax)*numel(xmin:xmax)*numel(zmin:zmax);
sumprod=sumprod/(countpairs);
sum1=sum1/(countpairs);
sum2=sum2/(countpairs);
Covariance(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)=sumprod – sum1*sum2;

%Standardize covariance values to correlogram
mean1=sum1;
mean2=sum2;
sumvar1=0;
sumvar2=0;
for k=zmin:zmax
for j=ymin:ymax
for i=xmin:xmax

sumvar1=(X(j,i,k)-mean1)^2 + sumvar1;
sumvar2=(X(j+hy,i+hx,k+hz)-mean2)^2 + sumvar2;

end
end
end

sumvar1=sumvar1/countpairs;
sumvar2=sumvar2/countpairs;

Correlogram(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)=Covariance(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)/sqrt(sumvar1*sumvar2);

end
end
end
end

I first compared these codes for a 2D input image (nz=1) and noticed that my new function runs much slower than the original function:
ExhaustiveCovarianceFunction(testslice,25): Elapsed time is 0.057659 seconds.
ExhaustiveCovarianceFunction3D(testslice,[25,25,0]): Elapsed time is 19.251866 seconds.
After some testing, this led me to realize that indexing a 3D array is much slower than a 2D array in MATLAB, and that this has something to do with how memory is accessed for higher-dimensional arrays. I found out that, if I added a third dimension to the original ExhaustiveCovarianceFunction with index 1 that never changed (eg, X(j,i,1), with no other changes, the code slowed down significantly:
2D array index X(j,i): Elapsed time is 0.059815 seconds.
3D array index X(j,i,1): Elapsed time is 18.849217 seconds.
The idea that we cannot work with higher-dimensional arrays in MATLAB if we want to have optimal performance led me to an approach where, in my new function, I convert the 2D and 3D arrays to a 1D array and map the nD array indices to 1D:
function index1D = convert3Dto1D_index(j, i, k, ny, nx)
index1D = j + (i – 1) * ny + (k – 1) * ny * nx;
end

function [Correlogram] = ExhaustiveCovarianceFunction3D(Xinput,lags)

X = flatten3D(Xinput);

[ny,nx,nz]=size(Xinput);

%lags is now a vector
Covariance=NaN([2*lags(1)+1, 2*lags(2)+1, 2*lags(3)+1]);
Correlogram=NaN([2*lags(1)+1, 2*lags(2)+1, 2*lags(3)+1]);

for hz=-lags(3):lags(3)
for hy=-lags(1):lags(1)
for hx=-lags(2):lags(2)

hvector = [hy hx hz];

if hvector(1)<0
ymin=abs(hvector(1))+1;
ymax=ny;
else
ymin=1;
ymax=ny-hvector(1);
end

if hvector(2)<0
xmin=abs(hvector(2))+1;
xmax=nx;
else
xmin=1;
xmax=nx-hvector(2);
end

if hvector(3)<0
zmin=abs(hvector(3))+1;
zmax=nz;
else
zmin=1;
zmax=nz-hvector(3);
end

sumprod=0;
sum1=0;
sum2=0;
countpairs=0;
for k=zmin:zmax
for j=ymin:ymax
for i=xmin:xmax
sumprod=X(convert3Dto1D_index(j, i, k, ny, nx))*X(convert3Dto1D_index(j+hy, i+hx, k+hz, ny, nx)) + sumprod;
sum1=X(convert3Dto1D_index(j, i, k, ny, nx)) + sum1;
sum2=X(convert3Dto1D_index(j+hy, i+hx, k+hz, ny, nx)) + sum2;
countpairs=countpairs+1;
end
end
end

countpairs = numel(ymin:ymax)*numel(xmin:xmax)*numel(zmin:zmax);
sumprod=sumprod/(countpairs);
sum1=sum1/(countpairs);
sum2=sum2/(countpairs);
Covariance(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)=sumprod – sum1*sum2;

%Standardize covariance values to correlogram
mean1=sum1;
mean2=sum2;
sumvar1=0;
sumvar2=0;
for k=zmin:zmax
for j=ymin:ymax
for i=xmin:xmax

sumvar1=(X(convert3Dto1D_index(j, i, k, ny, nx))-mean1)^2 + sumvar1;
sumvar2=(X(convert3Dto1D_index(j+hy, i+hx, k+hz, ny, nx))-mean2)^2 + sumvar2;

end
end
end

sumvar1=sumvar1/countpairs;
sumvar2=sumvar2/countpairs;

Correlogram(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)=Covariance(hy+lags(1)+1,hx+lags(2)+1, hz+lags(3)+1)/sqrt(sumvar1*sumvar2);

end
end
end
end
This approach has better performance, but is still slower than the original 2D code:
2D: Elapsed time is 0.163243 seconds.
3D, 3D index: Elapsed time is 18.336108 seconds.
3D, 1D index: Elapsed time is 0.431890 seconds.
The optimized code with 1D array indexing is still about 3x slower. Perhaps calling convert3Dto1D_index(j, i, k, ny, nx) every time the image index is called is leading to this expense.These computational concerns are important for larger images (eg, 256x256x128) and for higher-order statistics that will be developed.
Is there a smarter approach to addressing this problem? I cannot figure out how to speed up this 3D code any more. Ideally, I seek to make the 3D/general code to have comparable speeds to the 2D "hard-coded" problem when a 2D image is input. If this is not possible, separate subroutines for 2D and 3D images is likely my best bet. computation time, performance, time complexity, bigo, arrays, 2d, 3d, algorithm optimization MATLAB Answers — New Questions

​

Is it possible to "reset" MATLAB? Sometimes I want to "restore" MATLAB to the way it is when it is launched (not the way it was when it is installed). Closing all the figures, resetting the path and clearing variables is relatively easy, but not as easy as:

close all; clear all; path(pathdef); clc;

You need extra flags since the "all" flag is not really all (e.g., a figure might be hidden or mfiles files might be locked).

Resetting non-persistent "default" values is harder. For example, if at some point the "DefaultFigurePosition" is modified:

set(0, ‘DefaultFigurePosition’, [100, 100, 100, 100])

that change needs to be identified and reversed.

The list of things to get a full reset seems long to me. There are also issues about do I want to restore MATLAB to the way it was when it started or the way it will be the next time it starts. At this point I would be happy with either (or a mix).Is it possible to "reset" MATLAB? Sometimes I want to "restore" MATLAB to the way it is when it is launched (not the way it was when it is installed). Closing all the figures, resetting the path and clearing variables is relatively easy, but not as easy as:

close all; clear all; path(pathdef); clc;

You need extra flags since the "all" flag is not really all (e.g., a figure might be hidden or mfiles files might be locked).

Resetting non-persistent "default" values is harder. For example, if at some point the "DefaultFigurePosition" is modified:

set(0, ‘DefaultFigurePosition’, [100, 100, 100, 100])

that change needs to be identified and reversed.

The list of things to get a full reset seems long to me. There are also issues about do I want to restore MATLAB to the way it was when it started or the way it will be the next time it starts. At this point I would be happy with either (or a mix). Is it possible to "reset" MATLAB? Sometimes I want to "restore" MATLAB to the way it is when it is launched (not the way it was when it is installed). Closing all the figures, resetting the path and clearing variables is relatively easy, but not as easy as:

close all; clear all; path(pathdef); clc;

You need extra flags since the "all" flag is not really all (e.g., a figure might be hidden or mfiles files might be locked).

Resetting non-persistent "default" values is harder. For example, if at some point the "DefaultFigurePosition" is modified:

set(0, ‘DefaultFigurePosition’, [100, 100, 100, 100])

that change needs to be identified and reversed.

The list of things to get a full reset seems long to me. There are also issues about do I want to restore MATLAB to the way it was when it started or the way it will be the next time it starts. At this point I would be happy with either (or a mix). startup, function MATLAB Answers — New Questions

​

Why i dont get the same simulink blocs and interface when i run slrtExplorer in matlab R2020b as my Friend despite that we have the same version of matlabWhy i dont get the same simulink blocs and interface when i run slrtExplorer in matlab R2020b as my Friend despite that we have the same version of matlab Why i dont get the same simulink blocs and interface when i run slrtExplorer in matlab R2020b as my Friend despite that we have the same version of matlab transferred MATLAB Answers — New Questions

​

Hi all,
I have a laptop with the following configuration:
CPU: i7-11850H
RAM: 32GB
GPUs: Intel UHD graphics and NVIDIA RTX A2000

I notice that my laptos is pretty slow especially when managing figures. Indeed, by running bench command, the relative speed is 5.78 (this is the output of bench command 0.8408 0.3923 0.3292 0.6592 6.4034 7.0999) and my system lag hugely with respect the reference machines in 2-D and 3-D performance. When running bench command, the CPU usage peaked 18%. From this data, I believe that my system mostly run with Intel graphics rather on on my NVidia. Is that possible to verify which GPU card is running when Matlab is processing?
Thanks for your help.Hi all,
I have a laptop with the following configuration:
CPU: i7-11850H
RAM: 32GB
GPUs: Intel UHD graphics and NVIDIA RTX A2000

I notice that my laptos is pretty slow especially when managing figures. Indeed, by running bench command, the relative speed is 5.78 (this is the output of bench command 0.8408 0.3923 0.3292 0.6592 6.4034 7.0999) and my system lag hugely with respect the reference machines in 2-D and 3-D performance. When running bench command, the CPU usage peaked 18%. From this data, I believe that my system mostly run with Intel graphics rather on on my NVidia. Is that possible to verify which GPU card is running when Matlab is processing?
Thanks for your help. Hi all,
I have a laptop with the following configuration:
CPU: i7-11850H
RAM: 32GB
GPUs: Intel UHD graphics and NVIDIA RTX A2000

I notice that my laptos is pretty slow especially when managing figures. Indeed, by running bench command, the relative speed is 5.78 (this is the output of bench command 0.8408 0.3923 0.3292 0.6592 6.4034 7.0999) and my system lag hugely with respect the reference machines in 2-D and 3-D performance. When running bench command, the CPU usage peaked 18%. From this data, I believe that my system mostly run with Intel graphics rather on on my NVidia. Is that possible to verify which GPU card is running when Matlab is processing?
Thanks for your help. matlab MATLAB Answers — New Questions

​

I’m using the saveas function to export a figure as an svg file. I have set the renderer to be painters but occasionally the output of text is rendered as curves in the svg file.
Everything works fine except when using greek letters in axis labels (which I have avoided) or when the axis label contains exponents automatically by MATLAB. If I delete the " x 10^5 " part manually in the figure window or in the code I include ax = gca; ax.YAxis.Exponent = 0, then the saveas works fine exporting an svg file with text rendered as text. However, this is still a hassle and I’m hoping it can be fixed.
I’m using R2024a.I’m using the saveas function to export a figure as an svg file. I have set the renderer to be painters but occasionally the output of text is rendered as curves in the svg file.
Everything works fine except when using greek letters in axis labels (which I have avoided) or when the axis label contains exponents automatically by MATLAB. If I delete the " x 10^5 " part manually in the figure window or in the code I include ax = gca; ax.YAxis.Exponent = 0, then the saveas works fine exporting an svg file with text rendered as text. However, this is still a hassle and I’m hoping it can be fixed.
I’m using R2024a. I’m using the saveas function to export a figure as an svg file. I have set the renderer to be painters but occasionally the output of text is rendered as curves in the svg file.
Everything works fine except when using greek letters in axis labels (which I have avoided) or when the axis label contains exponents automatically by MATLAB. If I delete the " x 10^5 " part manually in the figure window or in the code I include ax = gca; ax.YAxis.Exponent = 0, then the saveas works fine exporting an svg file with text rendered as text. However, this is still a hassle and I’m hoping it can be fixed.
I’m using R2024a. svg, vector graphics, curves, axis labels MATLAB Answers — New Questions

​

Why does MATLAB R2021b or newer create a large directory of data for each user in ~/.MathWorks, %localappdata%MathWorks, or ~/Library/Application Support/MathWorks?Why does MATLAB R2021b or newer create a large directory of data for each user in ~/.MathWorks, %localappdata%MathWorks, or ~/Library/Application Support/MathWorks? Why does MATLAB R2021b or newer create a large directory of data for each user in ~/.MathWorks, %localappdata%MathWorks, or ~/Library/Application Support/MathWorks?  MATLAB Answers — New Questions

​

Why is the MathWorks Service Host causing issues with my cluster and/or HPC?Why is the MathWorks Service Host causing issues with my cluster and/or HPC? Why is the MathWorks Service Host causing issues with my cluster and/or HPC?  MATLAB Answers — New Questions

​

I’m encountering issues when trying to set the CoordinateSystem property for the sim3d.Actor object in Simulink. According to the documentation, this property should be configurable to use the MATLAB coordinate system, but it results in an error. I need guidance on the correct method to achieve this in the initialization script.
Additionally, I want to configure the Simulation 3D Scene Configuration block so that when selecting my Actor defined in the Simulation 3D Actor block as the Scene view, the view is in third person rather than the default coordinates [0 0 0].
Issue 1: Changing Coordinate System
I am trying to set the CoordinateSystem property for a sim3d.Actor object to use the MATLAB coordinate system. Here is the current initialization script:
fileName = "QuadCopter_Body.stl";

Body = sim3d.Actor(‘ActorName’, ‘Body’, …
‘Mobility’, sim3d.utils.MobilityTypes.Movable, …
‘ActorClassId’, sim3d.utils.SemanticType.Vehicle, …
‘CoordinateSystem’, ‘MATLAB’);

World.add(Body, Actor);

Body.load(fileName, [1 1 1]/100);
Body.Color = [0, 0, 1];
Body.Scale = [10 10 10];

Translation = [0.341 0.286 0.042;
-0.341 0.286 0.042;
0.341 -0.286 0.042;
-0.341 -0.286 0.042];

propellerFileName = "QuadCopter_Propeller.stl";

for propellerIndex = 1:4
actorName = sprintf(‘Propeller%d’, propellerIndex);

Propeller = sim3d.Actor(‘ActorName’,actorName, …
‘Mobility’, sim3d.utils.MobilityTypes.Movable, …
‘ActorClassId’, sim3d.utils.SemanticType.Vehicle);

World.add(Propeller, Actor);

Propeller.load(propellerFileName, [1 1 1]/100);
Propeller.Color = [1, 0, 0];
Propeller.Translation = Translation(propellerIndex, :);
Propeller.Rotation = [0 0 0 ];
Propeller.Scale = [10 10 10];
end

Actor.save("quadcopter.mat")
This is the error:
‘CoordinateSystem’ is not a recognized parameter. For a list of valid name-value pair argument, see the documentation for this function.

Issue 2: Setting Third-Person View
I also want to set the view in the Simulation 3D Scene Configuration block to be in third person when selecting my Actor defined in the Simulation 3D Actor block. Currently, the view defaults to the coordinates [0 0 0]. How can I change this view to a third-person perspective?I’m encountering issues when trying to set the CoordinateSystem property for the sim3d.Actor object in Simulink. According to the documentation, this property should be configurable to use the MATLAB coordinate system, but it results in an error. I need guidance on the correct method to achieve this in the initialization script.
Additionally, I want to configure the Simulation 3D Scene Configuration block so that when selecting my Actor defined in the Simulation 3D Actor block as the Scene view, the view is in third person rather than the default coordinates [0 0 0].
Issue 1: Changing Coordinate System
I am trying to set the CoordinateSystem property for a sim3d.Actor object to use the MATLAB coordinate system. Here is the current initialization script:
fileName = "QuadCopter_Body.stl";

Body = sim3d.Actor(‘ActorName’, ‘Body’, …
‘Mobility’, sim3d.utils.MobilityTypes.Movable, …
‘ActorClassId’, sim3d.utils.SemanticType.Vehicle, …
‘CoordinateSystem’, ‘MATLAB’);

World.add(Body, Actor);

Body.load(fileName, [1 1 1]/100);
Body.Color = [0, 0, 1];
Body.Scale = [10 10 10];

Translation = [0.341 0.286 0.042;
-0.341 0.286 0.042;
0.341 -0.286 0.042;
-0.341 -0.286 0.042];

propellerFileName = "QuadCopter_Propeller.stl";

for propellerIndex = 1:4
actorName = sprintf(‘Propeller%d’, propellerIndex);

Propeller = sim3d.Actor(‘ActorName’,actorName, …
‘Mobility’, sim3d.utils.MobilityTypes.Movable, …
‘ActorClassId’, sim3d.utils.SemanticType.Vehicle);

World.add(Propeller, Actor);

Propeller.load(propellerFileName, [1 1 1]/100);
Propeller.Color = [1, 0, 0];
Propeller.Translation = Translation(propellerIndex, :);
Propeller.Rotation = [0 0 0 ];
Propeller.Scale = [10 10 10];
end

Actor.save("quadcopter.mat")
This is the error:
‘CoordinateSystem’ is not a recognized parameter. For a list of valid name-value pair argument, see the documentation for this function.

Issue 2: Setting Third-Person View
I also want to set the view in the Simulation 3D Scene Configuration block to be in third person when selecting my Actor defined in the Simulation 3D Actor block. Currently, the view defaults to the coordinates [0 0 0]. How can I change this view to a third-person perspective? I’m encountering issues when trying to set the CoordinateSystem property for the sim3d.Actor object in Simulink. According to the documentation, this property should be configurable to use the MATLAB coordinate system, but it results in an error. I need guidance on the correct method to achieve this in the initialization script.
Additionally, I want to configure the Simulation 3D Scene Configuration block so that when selecting my Actor defined in the Simulation 3D Actor block as the Scene view, the view is in third person rather than the default coordinates [0 0 0].
Issue 1: Changing Coordinate System
I am trying to set the CoordinateSystem property for a sim3d.Actor object to use the MATLAB coordinate system. Here is the current initialization script:
fileName = "QuadCopter_Body.stl";

Body = sim3d.Actor(‘ActorName’, ‘Body’, …
‘Mobility’, sim3d.utils.MobilityTypes.Movable, …
‘ActorClassId’, sim3d.utils.SemanticType.Vehicle, …
‘CoordinateSystem’, ‘MATLAB’);

World.add(Body, Actor);

Body.load(fileName, [1 1 1]/100);
Body.Color = [0, 0, 1];
Body.Scale = [10 10 10];

Translation = [0.341 0.286 0.042;
-0.341 0.286 0.042;
0.341 -0.286 0.042;
-0.341 -0.286 0.042];

propellerFileName = "QuadCopter_Propeller.stl";

for propellerIndex = 1:4
actorName = sprintf(‘Propeller%d’, propellerIndex);

Propeller = sim3d.Actor(‘ActorName’,actorName, …
‘Mobility’, sim3d.utils.MobilityTypes.Movable, …
‘ActorClassId’, sim3d.utils.SemanticType.Vehicle);

World.add(Propeller, Actor);

Propeller.load(propellerFileName, [1 1 1]/100);
Propeller.Color = [1, 0, 0];
Propeller.Translation = Translation(propellerIndex, :);
Propeller.Rotation = [0 0 0 ];
Propeller.Scale = [10 10 10];
end

Actor.save("quadcopter.mat")
This is the error:
‘CoordinateSystem’ is not a recognized parameter. For a list of valid name-value pair argument, see the documentation for this function.

Issue 2: Setting Third-Person View
I also want to set the view in the Simulation 3D Scene Configuration block to be in third person when selecting my Actor defined in the Simulation 3D Actor block. Currently, the view defaults to the coordinates [0 0 0]. How can I change this view to a third-person perspective? sim3d, coordinatesystem, simulation3dactor, sceneconfiguration, simulink MATLAB Answers — New Questions

​

Im trying to solve a non-linear first order differential equation with ode45, with a weird function thrust_cont thats supposed to describe the thrust of a model rocket.

syms v(t) a(t) y(t) thrust_complete(t) t diff_equation(t,v) thrust_cont(t) thrust_cont(t)
thrust_clean = [0,0.176;0.001,0.198;0.002,0.381;0.003,0.414;0.004,0.176;0.005,0.104;0.006,0.27;0.007,0.17;0.008,0.201;0.009,0.107;0.01,0.248;0.011,0.159;0.012,0.1……..rest of the data; this is [time in ms, Force]
thrust_clean (1634:20000,:) = 0;
for n=1634:1:20000
thrust_clean (n:20000,1) = n/1000;
end
grad = 100;
cf = polyfit(thrust_clean(1:1700,1), thrust_clean(1:1700,2),grad);
thrust_complete = 0;
for g = 1:grad
thrust_complete = thrust_complete + cf(g)*t^(grad+1-g);
end
thrust_cont = heaviside(t) * thrust_complete * heaviside(1.633-t);
fplot(thrust_cont, [0,2])
m = 0.14;
C_probar = 2.3;
rho = 1.29;
A = pi*0.05*0.05;
C_d = 0.75;
span = [0,20];
diff_equation = thrust_cont/m – 9.8 -((C_d*rho*A*C_probar/(m*2))*(v(t)^2));
[t, flight] = ode45(@(t,v) diff_equation, span, 0)

in the bold highlighted line i have my final version of the continous thrust curve function, which i had to manipulate quite a bit (cause im not very good at matlab unfortunately). Then i define a couple of normal variables, and then the problem, i define my equation (which the right hand side is equal to the derivative of v), and I try to use the ode45 function, only for it to return the following error message:
Error using superiorfloat
Inputs must be floats, namely single or double.

Error in odearguments (line 114)
dataType = superiorfloat(t0,y0,f0);

Error in ode45 (line 107)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

Error in TBD_matlab (line 23)
[t, flight] = ode45(@(t,v) diff_equation, span, 0)

I don’t even understand what the error is referring to or even trying to tell me, and I’ve been trying for quite some time now to move things around but nothing seems to work. I previously actually had tried to use dsolve to get an answer, but it found no analytical solution. If anybody has the slightest idea what could be happening i’d be grateful 👍Im trying to solve a non-linear first order differential equation with ode45, with a weird function thrust_cont thats supposed to describe the thrust of a model rocket.

syms v(t) a(t) y(t) thrust_complete(t) t diff_equation(t,v) thrust_cont(t) thrust_cont(t)
thrust_clean = [0,0.176;0.001,0.198;0.002,0.381;0.003,0.414;0.004,0.176;0.005,0.104;0.006,0.27;0.007,0.17;0.008,0.201;0.009,0.107;0.01,0.248;0.011,0.159;0.012,0.1……..rest of the data; this is [time in ms, Force]
thrust_clean (1634:20000,:) = 0;
for n=1634:1:20000
thrust_clean (n:20000,1) = n/1000;
end
grad = 100;
cf = polyfit(thrust_clean(1:1700,1), thrust_clean(1:1700,2),grad);
thrust_complete = 0;
for g = 1:grad
thrust_complete = thrust_complete + cf(g)*t^(grad+1-g);
end
thrust_cont = heaviside(t) * thrust_complete * heaviside(1.633-t);
fplot(thrust_cont, [0,2])
m = 0.14;
C_probar = 2.3;
rho = 1.29;
A = pi*0.05*0.05;
C_d = 0.75;
span = [0,20];
diff_equation = thrust_cont/m – 9.8 -((C_d*rho*A*C_probar/(m*2))*(v(t)^2));
[t, flight] = ode45(@(t,v) diff_equation, span, 0)

in the bold highlighted line i have my final version of the continous thrust curve function, which i had to manipulate quite a bit (cause im not very good at matlab unfortunately). Then i define a couple of normal variables, and then the problem, i define my equation (which the right hand side is equal to the derivative of v), and I try to use the ode45 function, only for it to return the following error message:
Error using superiorfloat
Inputs must be floats, namely single or double.

Error in odearguments (line 114)
dataType = superiorfloat(t0,y0,f0);

Error in ode45 (line 107)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

Error in TBD_matlab (line 23)
[t, flight] = ode45(@(t,v) diff_equation, span, 0)

I don’t even understand what the error is referring to or even trying to tell me, and I’ve been trying for quite some time now to move things around but nothing seems to work. I previously actually had tried to use dsolve to get an answer, but it found no analytical solution. If anybody has the slightest idea what could be happening i’d be grateful 👍 Im trying to solve a non-linear first order differential equation with ode45, with a weird function thrust_cont thats supposed to describe the thrust of a model rocket.

syms v(t) a(t) y(t) thrust_complete(t) t diff_equation(t,v) thrust_cont(t) thrust_cont(t)
thrust_clean = [0,0.176;0.001,0.198;0.002,0.381;0.003,0.414;0.004,0.176;0.005,0.104;0.006,0.27;0.007,0.17;0.008,0.201;0.009,0.107;0.01,0.248;0.011,0.159;0.012,0.1……..rest of the data; this is [time in ms, Force]
thrust_clean (1634:20000,:) = 0;
for n=1634:1:20000
thrust_clean (n:20000,1) = n/1000;
end
grad = 100;
cf = polyfit(thrust_clean(1:1700,1), thrust_clean(1:1700,2),grad);
thrust_complete = 0;
for g = 1:grad
thrust_complete = thrust_complete + cf(g)*t^(grad+1-g);
end
thrust_cont = heaviside(t) * thrust_complete * heaviside(1.633-t);
fplot(thrust_cont, [0,2])
m = 0.14;
C_probar = 2.3;
rho = 1.29;
A = pi*0.05*0.05;
C_d = 0.75;
span = [0,20];
diff_equation = thrust_cont/m – 9.8 -((C_d*rho*A*C_probar/(m*2))*(v(t)^2));
[t, flight] = ode45(@(t,v) diff_equation, span, 0)

in the bold highlighted line i have my final version of the continous thrust curve function, which i had to manipulate quite a bit (cause im not very good at matlab unfortunately). Then i define a couple of normal variables, and then the problem, i define my equation (which the right hand side is equal to the derivative of v), and I try to use the ode45 function, only for it to return the following error message:
Error using superiorfloat
Inputs must be floats, namely single or double.

Error in odearguments (line 114)
dataType = superiorfloat(t0,y0,f0);

Error in ode45 (line 107)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

Error in TBD_matlab (line 23)
[t, flight] = ode45(@(t,v) diff_equation, span, 0)

I don’t even understand what the error is referring to or even trying to tell me, and I’ve been trying for quite some time now to move things around but nothing seems to work. I previously actually had tried to use dsolve to get an answer, but it found no analytical solution. If anybody has the slightest idea what could be happening i’d be grateful 👍 ode45, matlab, differential equations MATLAB Answers — New Questions

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